Here's what rhymes with assessable.
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ineffable sensible terrible cerebral flexible festival vegetable amenable decimal parable seminal legible ostensible tenable bearable testable wearable medical chemical acceptable susceptible credible perceptible retinal sectional sensual insensible sceptical unbearable untenable defensible illegible sentinel caramel inedible amendable breathable perfectible spendable stretchable weldable bendable comestible spreadable unwearable clerical perceptual spectacle skeptical textual commendable inflexible lamentable pedestal receptacle segmental attentional detestable impeccable polemical unforgettable alchemical digestible execrable obsessional presentable contestable dispensable extensible prophetical tentacle collectible correctable repairable suggestible collectable forgettable pentacle perceptional connectable electable connectible quenchable professional conventional numerical exceptional hypothetical incredible intestinal respectable plentiful unacceptable confessional dependable detectable directional correctional regrettable chimerical delectable expendable indefensible preventable concessional processional insusceptible conceptional convectional extendable recessional preventible detectible dimensional indispensable biochemical intentional contemptible impregnable reprehensible trigeminal extensional geochemical incontestable indigestible inflectional photochemical undetectable unquenchable paramedical undependable unexceptional inflexional premedical recommendable unpreventable complexional congressional heterosexual homosexual comprehensible unconventional unintentional bidirectional histochemical intertextual intracerebral physicochemical psychosexual unprofessional nonclerical nonnumerical noncollectable threedimensional twodimensional anticlerical nonprofessional subprofessional alphanumerical unidirectional paraprofessional semiprofessional gastrointestinal multidimensional immunohistochemical